I saw this for the first time on r/Bitcoin earlier today and become interested.
You are correct to look for the risk. It has been my goal to create as little need for trust of BitPools as possible with the end goal being a decentralized system (baby steps).
It sounds like I need to first have a funded BitPools account (in order to vote), so I assume that I need to trust BitPools not to run off with the bitcoin funds, correct?
You are correct that if you want to participate you must fund your BitPools account with bitcoins. However, there are two major game changers with BitPools. One is the voting and the other is how you fund your account.
You have full control over the bitcoins in your account. Read the demonstration on How To page on the site. You provide a bitcoin address with your funds. This is to verify that you have the funds in the first place to even participate in the discussion. BitPools never touches your bitcoins until you vote.
And then it sounds like if the proposal is accepted, the funds get transferred to the proposer's account, so I would also need to trust that the proposer would actually carry out the proposal and purchase the tickets, correct?
This is where the risk lies and you are trusting BitPools briefly on the vote date to transfer the funds (but to break this trust on one proposal and one vote would break the trust for the whole point of the site).
But yes, there is risk in trusting the proposer to follow through with what is essentially a contract with the voters. To mitigate the risk the plan is for the option of using escrow and multisig transactions for implementation of the proposals. The plan for the most secure proposal transaction would be having the voters designate a person or group to have control over one part of a multisig transaction, the proposer would have control over another part and a third party escrow service would hold the third. If the transaction goes through without a hitch, then the voters accept it and move the money. If there is a dispute the escrow service determines the outcome. As there are many different types of proposals I imagine there would be a lot of specialist escrow services (real estate, construction, businesses, generic, etc.)
As the site is young I have focused first on making things as simple as possible, the goal of first just getting people used to the concept on little projects. Proposers will need to prove to the voters that they are trustworthy and do what they can to demonstrate that there is little to no risk. And as time goes on I will continue to add functionality to help whittle that risk down to nothing.